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huber

Huber loss for regression tasks

Since R2021a

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    Syntax

    loss = huber(Y,targets)
    loss = huber(Y,targets,weights)
    loss = huber(___,'DataFormat',FMT)
    loss = huber(___,Name,Value)

    Description

    The Huber operation computes the Huber loss between network predictions and target values for regression tasks. When the 'TransitionPoint' option is 1, this is also known as smooth L1 loss.

    The huber function calculates the Huber loss using dlarray data. Using dlarray objects makes working with high dimensional data easier by allowing you to label the dimensions. For example, you can label which dimensions correspond to spatial, time, channel, and batch dimensions using the "S", "T", "C", and "B" labels, respectively. For unspecified and other dimensions, use the "U" label. For dlarray object functions that operate over particular dimensions, you can specify the dimension labels by formatting the dlarray object directly, or by using the DataFormat option.

    example

    loss = huber(Y,targets) returns the Huber loss between the formatted dlarray object Y containing the predictions and the target values targets for regression tasks. The input Y is a formatted dlarray. The output loss is an unformatted dlarray scalar.

    For unformatted input data, use the 'DataFormat' option.

    loss = huber(Y,targets,weights) applies weights to the calculated loss vales. Use this syntax to weight the contributions of classes, observations, or regions of the input to the calculated loss values.

    loss = huber(___,'DataFormat',FMT) also specifies the dimension format FMT when Y is not a formatted dlarray.

    loss = huber(___,Name,Value) specifies options using one or more name-value pair arguments in addition to the input arguments in previous syntaxes. For example, 'NormalizationFactor','all-elements' specifies to normalize the loss by dividing the reduced loss by the number of input elements.

    Examples

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    Open Live Script

    Create an array of predictions for 12 observations over 10 responses.

    numResponses = 10;
numObservations = 12;

Y = rand(numResponses,numObservations);
dlY = dlarray(Y,'CB');

    View the size and format of the predictions.

    size(dlY)
    ans = 1×2

    10    12


    dims(dlY)
    ans = 
'CB'

    Create an array of random targets.

    targets = rand(numResponses,numObservations);

    View the size of the targets.

    size(targets)
    ans = 1×2

    10    12

    Compute the Huber loss between the predictions and the targets.

    loss = huber(dlY,targets)
    loss = 
  1x1 dlarray

    0.7374
    Open Live Script

    Create arrays of predictions and targets for 12 sequences of varying lengths over 10 responses.

    numResponses = 10;
numObservations = 12;
maxSequenceLength = 15;

sequenceLengths = randi(maxSequenceLength,[1 numObservations]);

Y = cell(numObservations,1);
targets = cell(numObservations,1);

for i = 1:numObservations
    Y{i} = rand(numResponses,sequenceLengths(i));
    targets{i} = rand(numResponses,sequenceLengths(i));
end

    View the cell arrays of predictions and targets.

    Y
    Y=12×1 cell array
    {10x13 double}
    {10x14 double}
    {10x2  double}
    {10x14 double}
    {10x10 double}
    {10x2  double}
    {10x5  double}
    {10x9  double}
    {10x15 double}
    {10x15 double}
    {10x3  double}
    {10x15 double}


    targets
    targets=12×1 cell array
    {10x13 double}
    {10x14 double}
    {10x2  double}
    {10x14 double}
    {10x10 double}
    {10x2  double}
    {10x5  double}
    {10x9  double}
    {10x15 double}
    {10x15 double}
    {10x3  double}
    {10x15 double}

    Pad the prediction and target sequences in the second dimension using the padsequences function and also return the corresponding mask.

    [Y,mask] = padsequences(Y,2);
targets = padsequences(targets,2);

    Convert the padded sequences to dlarray with format 'CTB' (channel, time, batch). Because formatted dlarray objects automatically sort the dimensions, keep the dimensions of the targets and mask consistent by also converting them to a formatted dlarray objects with the same formats.

    dlY = dlarray(Y,'CTB');
targets = dlarray(targets,'CTB');
mask = dlarray(mask,'CTB');

    View the sizes of the prediction scores, targets, and the mask.

    size(dlY)
    ans = 1×3

    10    12    15


    size(targets)
    ans = 1×3

    10    12    15


    size(mask)
    ans = 1×3

    10    12    15

    Compute the Huber loss between the predictions and the targets. To prevent the loss values calculated from padding from contributing to the loss, set the 'Mask' option to the mask returned by the padsequences function.

    loss = huber(dlY,targets,'Mask',mask)
    loss = 
  1x1 dlarray

    8.1834

    Input Arguments

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    Predictions, specified as a formatted dlarray, an unformatted dlarray, or a numeric array. When Y is not a formatted dlarray, you must specify the dimension format using the DataFormat option.

    If Y is a numeric array, targets must be a dlarray.

    Target responses, specified as a formatted or unformatted dlarray or a numeric array.

    The size of each dimension of targets must match the size of the corresponding dimension of Y.

    If targets is a formatted dlarray, then its format must be the same as the format of Y, or the same as DataFormat if Y is unformatted.

    If targets is an unformatted dlarray or a numeric array, then the function applies the format of Y or the value of DataFormat to targets.

    Tip

    Formatted dlarray objects automatically permute the dimensions of the underlying data to have order "S" (spatial), "C" (channel), "B" (batch), "T" (time), then "U" (unspecified). To ensure that the dimensions of Y and targets are consistent, when Y is a formatted dlarray, also specify targets as a formatted dlarray.

    Weights, specified as a dlarray or a numeric array.

    To specify response weights, specify a vector with a 'C' (channel) dimension with size matching the 'C' (channel) dimension of the Y. Specify the 'C' (channel) dimension of the response weights by using a formatted dlarray object or by using the 'WeightsFormat' option.

    To specify observation weights, specify a vector with a 'B' (batch) dimension with size matching the 'B' (batch) dimension of the Y. Specify the 'B' (batch) dimension of the class weights by using a formatted dlarray object or by using the 'WeightsFormat' option.

    To specify weights for each element of the input independently, specify the weights as an array of the same size as Y. In this case, if weights is not a formatted dlarray object, then the function uses the same format as Y. Alternatively, specify the weights format using the 'WeightsFormat' option.

    Name-Value Arguments

    Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

    Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

    Example: 'NormalizationFactor','all-elements' specifies to normalize the loss by dividing the reduced loss by the number of input elements

    Point where Huber loss transitions from a quadratic function to a linear function, specified as the comma-separated pair consisting of 'TransitionPoint' and a positive scalar.

    When 'TransitionPoint' is 1, this is also known as smooth L1 loss.

    Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

    Mask indicating which elements to include for loss computation, specified as a dlarray object, a logical array, or a numeric array with the same size as Y.

    The function includes and excludes elements of the input data for loss computation when the corresponding value in the mask is 1 and 0, respectively.

    If Mask is a formatted dlarray object, then its format must match that of Y. If Mask is not a formatted dlarray object, then the function uses the same format as Y.

    If you specify the DataFormat option, then the function also uses the specified format for the mask.

    The size of each dimension of Mask must match the size of the corresponding dimension in Y. The default value is a logical array of ones.

    Tip

    Formatted dlarray objects automatically permute the dimensions of the underlying data to have this order: "S" (spatial), "C" (channel), "B" (batch), "T" (time), and "U" (unspecified). For example, dlarray objects automatically permute the dimensions of data with format "TSCSBS" to have format "SSSCBT".

    To ensure that the dimensions of Y and the mask are consistent, when Y is a formatted dlarray, also specify the mask as a formatted dlarray.

    Mode for reducing the array of loss values, specified as one of the following:

    • "sum" — Sum all of the elements in the array of loss values. In this case, the output loss is scalar.

    • "none" — Do not reduce the array of loss values. In this case, the output loss is an unformatted dlarray object with the same size as Y.

    Divisor for normalizing the reduced loss when Reduction is "sum", specified as one of the following:

    • "batch-size" — Normalize the loss by dividing it by the number of observations in Y.

    • "all-elements" — Normalize the loss by dividing it by the number of elements of Y.

    • "mask-included" — Normalize the loss by dividing the loss values by the number of included elements specified by the mask for each observation independently. To use this option, you must specify a mask using the Mask option.

    • "none" — Do not normalize the loss.

    Dimension order of unformatted input data, specified as a character vector or string scalar FMT that provides a label for each dimension of the data.

    When you specify the format of a dlarray object, each character provides a label for each dimension of the data and must be one of these options:

    • "S" — Spatial

    • "C" — Channel

    • "B" — Batch (for example, samples and observations)

    • "T" — Time (for example, time steps of sequences)

    • "U" — Unspecified

    You can specify multiple dimensions labeled "S" or "U". You can use the labels "C", "B", and "T" at most once.

    You must specify DataFormat when the input data is not a formatted dlarray.

    Data Types: char | string

    Dimension order of the weights, specified as a character vector or string scalar that provides a label for each dimension of the weights.

    When you specify the format of a dlarray object, each character provides a label for each dimension of the data and must be one of these options:

    • "S" — Spatial

    • "C" — Channel

    • "B" — Batch (for example, samples and observations)

    • "T" — Time (for example, time steps of sequences)

    • "U" — Unspecified

    You can specify multiple dimensions labeled "S" or "U". You can use the labels "C", "B", and "T" at most once.

    You must specify WeightsFormat when weights is a numeric vector and Y has two or more nonsingleton dimensions.

    If weights is not a vector, or both weights and Y are vectors, then default value of WeightsFormat is the same as the format of Y.

    Data Types: char | string

    Output Arguments

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    Huber loss, returned as an unformatted dlarray. The output loss is an unformatted dlarray with the same underlying data type as the input Y.

    The size of loss depends on the Reduction option.

    Algorithms

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    Huber Loss

    For each element Yj of the input, the huber function computes the corresponding element-wise loss values using the formula

    lossj={12(Yj−Tj)2if |Yj−Tj|≤δδ|Yj−Tj|−12δ2otherwise,

    where Tj is the corresponding target value to the prediction Yj and δ is the transition point where the loss transitions from a quadratic function to a linear function.

    When the transition point is 1, this is also known as smooth L1 loss.

    To reduce the loss values to a scalar, the function then reduces the element-wise loss using the formula

    loss=1N∑jmjwjlossj,

    where N is the normalization factor, mj is the mask value for element j, and wj is the weight value for element j.

    If you do not opt to reduce the loss, then the function applies the mask and the weights to the loss values directly:

    lossj*=mjwjlossj

    Extended Capabilities

    Version History

    Introduced in R2021a

    See Also

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